In[]:=
eqlist={(Quantity[(4π)/tNow,1/("Seconds")])Sin[(9.419*10^-21tNow)/​​    Sqrt[1/CMBRTempAtStart^4]]==​​  Quantity[(37π)/48469710106800000000,1/("Seconds")],​​1/(22^(1/4)​​     Sqrt[π])(((1+​​         Cos[(2.9592*10^-20tNow)/Sqrt[1/​​          CMBRTempAtStart^4]])(Quantity[​​         6.399*10^59,("Kelvins")^4("Meters")^2]))/(Cos[(​​         9.419*10^-21tNow)/Sqrt[1/​​         CMBRTempAtStart^4]](Quantity[-3.9996*10^29Sqrt[1/​​           CMBRTempAtStart^4],"Meters"])+​​       Quantity[4.636*10^29Sqrt[1/CMBRTempAtStart^4],"Meters"])^2)^(​​   1/4)==Quantity[2.73,"Kelvins"]} 
Out[]=

4π
tNow
per second
Sin
9.419×
-21
10
tNow
1
4
CMBRTempAtStart

37π
48469710106800000000
per second
,
1
2
1/4
2
π
1/4
1+Cos
2.9592×
-20
10
tNow
1
4
CMBRTempAtStart

6.399×
59
10
2
m
4
K

2
Cos
9.419×
-21
10
tNow
1
4
CMBRTempAtStart

-3.9996×
29
10
1
4
CMBRTempAtStart
m
+
4.636×
29
10
1
4
CMBRTempAtStart
m

2.73
K

In[]:=
FindRoot[eqlist,{{tNow,5*356.25*3600*24*10^10},{CMBRTempAtStart,3}}]
FindRoot
:-- Message text not found -- ​1.539×
18
10
,3.​ (​{tNow,CMBRTempAtStart}​) ​
-1.33593×
-18
10
per second
,
0.1626
K
​ (​{2}​) (​Removed[$$Failure]​)
FindRoot
:-- Message text not found -- ​1.539×
18
10
,3.​ (​{tNow,CMBRTempAtStart}​) ​
-1.33593×
-18
10
per second
,
0.1626
K
​ (​{2}​) (​Removed[$$Failure]​)
FindRoot
:-- Message text not found -- ​1.539×
18
10
,3.​ (​{tNow,CMBRTempAtStart}​) ​
-1.33593×
-18
10
per second
,
0.1626
K
​ (​{2}​) (​Removed[$$Failure]​)
General
:Further output of FindRoot::nlu will be suppressed during this calculation.
FindRoot
:-- Message text not found -- ​1.539×
18
10
,3.​ (​{tNow,CMBRTempAtStart}​) ​
-1.33593×
-18
10
per second
,
0.1626
K
​ (​{2}​) (​Removed[$$Failure]​)
FindRoot
:-- Message text not found -- ​1.539×
18
10
,3.​ (​{tNow,CMBRTempAtStart}​) ​
-1.33593×
-18
10
per second
,
0.1626
K
​ (​{2}​) (​Removed[$$Failure]​)
Out[]=
FindRoot[eqlist,{{tNow,5×356.25×3600×24
10
10
},{CMBRTempAtStart,3}}]
FindRoot
:-- Message text not found -- ​1.539×
18
10
,3.​ (​{tNow,CMBRTempAtStart}​) ​
-1.33593×
-18
10
per second
,
0.1626
K
​ (​{2}​) (​Removed[$$Failure]​)
FindRoot
:-- Message text not found -- ​1.539×
18
10
,3.​ (​{tNow,CMBRTempAtStart}​) ​
-1.33593×
-18
10
per second
,
0.1626
K
​ (​{2}​) (​Removed[$$Failure]​)
FindRoot
:-- Message text not found -- ​1.539×
18
10
,3.​ (​{tNow,CMBRTempAtStart}​) ​
-1.33593×
-18
10
per second
,
0.1626
K
​ (​{2}​) (​Removed[$$Failure]​)
General
:Further output of FindRoot::nlu will be suppressed during this calculation.